Locally Linear Denoising on Image Manifolds

We study the problem of image denoising where images are assumed to be samples from
low dimensional (sub)manifolds. We propose the algorithm of locally linear denoising. The
algorithm approximates manifolds with locally linear patches by constructing nearest
neighbor graphs. Each image is then locally denoised within its neighborhoods. A global
optimal denoising result is then identified by aligning those local estimates. The algorithm
has a closed-form solution that is efficient to compute. We evaluated and compared the
algorithm to alternative methods on two image data sets. We demonstrated the effectiveness
of the proposed algorithm, which yields visually appealing denoising results, incurs
smaller reconstruction errors and results in lower error rates when the denoised data are used in supervised learning tasks.